n Distinguishable Particles on the Real Line interacting via Two Body Delta Potentials

Abstract

This paper studies a system of $n \in \mathbb{N}: \, n \geq 2$ non-relativistic, spinless quantum particles moving on the real line and interacting via a two-body delta potential. The Hamiltonian of such a system is proved to be affiliated to the resolvent algebra of the case, $\mathcal{R}\left( \mathbb{R}^{2n},\sigma \right)$; it is further shown the existence of a $\text{C}^{\ast}-$dynamical system and of a subalgebra $\pi_S\left( \mathfrak{S}_0 \right)^{-1} \subset \mathcal{R}\left( \mathbb{R}^{2n},\sigma \right)$, stable under time evolution, where $\pi_S$ is the Schr{\"o}dinger representation of the algebra.